Classification in Hilbert Spaces with Support Vector Machines

International audienceIn many applications, input data are in fact sampled functions rather than standard high dimensional vectors. Most of the traditional data analysis tools for regression, classification and clustering have been adapted to handle functional inputs under the general name of Functional Data Analysis (FDA). In general, the major problem is to overcome the issue of infinite dimensional input. This is done by introducing regularity constraints on the studied functions, thanks to penalization or to projection on finite dimensional functional spaces. Support Vector Machine (SVM) are large margin classifier tools that have the interesting property of being less sensitive to the curse of dimensionality than other tools. On the contrary, they are based on implicit non linear mappings of the considered data into high dimensional spaces (sometimes with infinite dimension) thanks to kernel functions. In this paper, we investigate the use of Support Vector Machine for functional data analysis. We define simple kernels that take into account the functional nature of the data and lead to consistent classification. Experiments conducted on real world data emphasize the benefit of taking into account some functional aspects of the problems